Hi,
I have the same problem. Specific letters like Č, Ė, Į, Ų, Ū (č, ė, į, ų, ū)are of a different font.
I am a beginer, so I don’t really know what to do. I am using twenty fourteen theme. Here is a link of a post showing how exactly it looks like now: http://www.sedile.lt/naujienos/aa-aa-cc-cc-eee-eee-ii-ii-ss-ss-uuu-uuu-zz-zz/.
Would it help if I add letters I need to this font by myself?
Well, it worked out that way. I installed a plugin WordPress Font Uploader and uploaded all the fonts (10 in total) that I edited from Lato family in OTF format. I only added those Lithuanian letters that were not there, so it will help only Lithuanians. It isn’t a professional work, however I am satisfied enough with it. You can download and see how it looks here http://www.sedile.lt/naujienos/aa-aa-cc-cc-eee-eee-ii-ii-ss-ss-uuu-uuu-zz-zz/.
In plugin I set the font to Lato-Reg.otf everywhere.